5. Decide whether each equation is true for all, one, or no values of x.

Determine the type and number of solutions of −4x2 − 3x + 7 = 0.

Kaylis [27]

Answer:

Step-by-step explanation:

You have to use the discriminant for this. If the quadratic is $-4x^2-3x+7$ , then

a = -4, b = -3, and c = 7. The formula for finding the discriminant is

$D=b^2-4ac$ which comes from the quadratic formula, but without the square root sign. Filling in:

$D=(-3)^2-4(-4)(7)$ which simplifies down to

D = 9 + 112 so

D = 121. This is a perfect square, so the solutions will be 2 real. Just so you know, you will NEVER have a solution like the one offered in the third choice down. If you have one imaginary root, you will ALWAYS have a second by the conjugate rule.

7 0

3 years ago

Among cases of heart pacemaker malfunctions, were found to be caused by firmware, which is software programmed into the device.

alex41 [277]

Complete question is;

Among 8834 cases of heart pacemaker malfunctions, 504 were found to be caused by firmware, which is software programmed into the device. If the firmware is tested in three different pacemakers randomly selected from this batch of 8834 and the entire batch is accepted if there are no failures, what is the probability that the firmware in the entire batch will be accepted? Is this procedure likely to result in the entire batch being accepted?

Answer:

P(All three are not caused by firmware) = 83.84%

Probability that the entire batch will be accepted = 0.8384

Step-by-step explanation:

We are told that out of the 8834 cases of heart pacemaker malfunctions, 504 were found to be caused by firmware.

Thus,

Cases not caused by firmware = 8834 - 504 = 8330

So, probability of the first case not being affected by firmware is;

P(first case not caused by firmware) = 8330/8834

Also,

Probability of second case not being affected by firmware is given as;

P(second case not caused by firmware|first case not affected by firmware) = 8329/8833

Similarly,

Probability of third case not being affected by firmware is given as;

P(third case not caused by firmware|first and second not caused by firmware) = 8328/8832

Now, looking at the 3 Probabilities gotten, it is obvious that the events are not independent because the probability of occurence of one event depends on the probability of occurence of the other event.

Thus, we will make use of the general multiplication rule which is;

P(A & B) = P(B) × P(A|B)

Thus;

P(All three not caused by firmware) = P(first case not caused by firmware) × P(second case not caused by firmware|first case not affected by firmware) × P(third case not caused by firmware|first and second not caused by firmware)

Plugging in the relevant values, we have;

P(All three not caused by firmware) = (8330/8834) × (8329/8833) × (8328/8832)

P(All three are not caused by firmware) = 0.83840506679 ≈ 83.84%

6 0

3 years ago

Which graph represents a function with an initial value of One-half?

sweet [91]

Answer:

The answer is B

Step-by-step explanation:

I went on socratic and found the answer

7 0

3 years ago

Hatah and his 3 friends are each running an equal part of a la mile race.

Lana71 [14]

Answer:3.5 miles

Step-by-step explanation:

8 0

3 years ago

A cart is coasting past Gordon. As it passes, he exerts a force on it. Whether the cart speeds up, slows down, or changes direct

Ksivusya [100]

Answer:

Direction

Step-by-step explanation:

Whether the car slows down or speeds up depends on the direction of the force applied, because if Gordon applied the force opposite the direction of the cart's movement, then the cart will slow down. If however, the force is applied in the direction of the carts movement, then the cart will speed up.

6 0

3 years ago